Estimating process capability indices using ridge regression

Abstract

Process capability indices show the ability of a process to produce products according to the pre-specified requirements. Since final quality characteristics of a product are usually interrelated to its previous amounts in earlier workstations, one need to model and consider the relationship among them to assess the process ca-pability properly. Hence, conducting process capability analysis in multivariate environment is inevitable; unfortunately, the analysis in multivariate environment is usually complex and requires extensive calcula-tions. Sometimes it is preferable to simplify the analysis by assuming independency among quality character-istics and evaluating process performance with respect to each individual quality characteristic using univari-ate process capability indices such as CP, CPK, CPM, and CPMK. However, this simplification introduces some error in the analysis leading to under or overestimation of the process capability index. This paper models the interrelationship among quality characteristics that are produced in different workstations to provide an over-all process capability index. Ridge residual regression is used as a vehicle to evaluate process capability and helps quality engineers to provide a reasonable quality policy for controlling and reducing variation in quality characteristics.